Congress has no shortage of trouble moving big-ticket legislation, so it might be preposterous to think the Senate can move forward on replacing the education law known most recently as No Child Left Behind.

But, the Senate might have the right partners to pull it off. Health, Education, Labor and Pensions Chairman Lamar Alexander, R-Tenn., and ranking member Patty Murray, D-Wash., announced an agreement over the recess, and they're moving full-speed ahead with a Tuesday markup.

"Chairman Alexander and ranking member Murray working together on education demonstrates what can happen when committees are allowed to work. This is the tradition of the Senate and who better to help restore regular order than these two hard-working, savvy senators who have the respect of their peers and of each other," said one Republican leadership aide.

The agreement is far from what either side would have written — Murray is a former preschool teacher who has advocated for a much broader program to support pre-K and other early learning activities, and Alexander once ran for president on a platform that included eliminating the Department of Education as we know it.

But Alexander and Murray are proven legislators.

"She's smart, she cares about children, and she's results-oriented," Alexander said of his ranking member. "And she has respect within her conference."

There's no doubt the respect is mutual.

"As Chairman Alexander and I adjust to our new roles, I think we have one belief we have mentioned every time we talk: We think working together, this committee can really get some exciting work done over the next couple years," Murray said at a HELP hearing in January.

Alexander released a discussion draft in January without Democratic support and a public disagreement about the way forward. But Alexander said Murray suggested the two sides get together before proceeding to what could've become a partisan, charged markup.

"I thought she had a good idea, because we've been trying this now for six years without success, and it turned out to be a good idea because the more we studied it, it was a complicated problem with a really simple solution," Alexander said in an interview with CQ Roll Call. "We keep ... the important measurements of student achievement, but we restore to states the responsibility for deciding what to do about the results of those tests."

The two senators came together on the way forward, but it remains early in the process, and their deal has critics on both sides — but Alexander said they were listening to fellow senators, including Rand Paul. The Kentucky Republican is among those seeking the presidency in 2016, and he has been highlighting his opposition to the curriculum standards, deriding Common Core in one Web video as "a hodgepodge of educational theories, bureaucratic groupthink, massive data collection and pure secular statist propaganda."

"Sen. Paul, for example, wanted to make sure that Common Core is voluntary, so we listened to him and he'll be offering an amendment on that," Alexander said.

And on the other side, while the liberal Center for American Progress praised Alexander and Murray for some provisions of the bill, Executive Vice President for Policy Carmel Martin also made a call for improvements through the legislative process.

"It eliminates virtually all obligations for states and school districts to intervene and provide support to schools with large achievement gaps or their lowest-performing schools. And finally, it does nothing to create incentives for states and school districts to examine their assessment systems to eliminate harmful, duplicative, or low-quality tests," Martin said in a statement.

But, while threading the needle may be tough, there's been talk on and off Capitol Hill that if Alexander and Murray get an acceptable product through the committee in short order, it could reach the floor as early as the current work period (which runs up to Memorial Day).

Both senators recognize the need to hold back on what they would propose in an ideal world, and they're hoping their colleagues will do likewise.

Alexander recalled during his time as governor of Tennessee a successful effort to allow for teachers to earn merit-based pay. That effort required winning the backing of a Democratic-led Legislature, which meant taking an amendment from a Democratic speaker of the state House.

"I learned then that if you want to get a result, you have to listen to other people, and when we have a Democratic president and when we have a Senate ... in which you need 60 votes, the people you need to listen to include Democrats as well as Republicans," Alexander said.

That trust comes from experience. Alexander's a former secretary of Education who has served in the GOP leadership and Murray, the current No. 4 in Democratic leadership, also has a bipartisan track record, most notably as the lead Democratic negotiator in the bipartisan budget negotiations with Rep. Paul D. Ryan, R-Wis.

Murray promoted the latest effort after an event with college students in Yakima, Wash., during the recess.

"There is absolutely nobody in this country that thinks the current law is working," Murray said. "We've been hit dramatically in our state by some of the provisions in No Child Left Behind. And Senator Lamar Alexander, a Republican, and I have put together a bipartisan bill to fix some of the provisions of No Child Left Behind so that we can actually help our students succeed in a more positive way."